Question: Simplify the following expression: $ r = \dfrac{-8}{5} + \dfrac{-6x + 9}{-5x} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5x}{-5x}$ $ \dfrac{-8}{5} \times \dfrac{-5x}{-5x} = \dfrac{40x}{-25x} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-6x + 9}{-5x} \times \dfrac{5}{5} = \dfrac{-30x + 45}{-25x} $ Therefore $ r = \dfrac{40x}{-25x} + \dfrac{-30x + 45}{-25x} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{40x - 30x + 45}{-25x} $ $r = \dfrac{10x + 45}{-25x}$ Simplify the expression by dividing the numerator and denominator by -5: $r = \dfrac{-2x - 9}{5x}$